This work introduces a new class of particle filters, that include an auxiliary Markov transition in their design. Actually, it was motivated by potential application to multitarget tracking, but the solution provided may be of practical interest elsewhere. This work also shows how to include a crossover step in sequential Monte Carlo methods. It is well known that sequential Monte Carlo methods can be interpreted in terms of implementing selection and mutation steps, using the language of evolutionary algorithms. However, most general evolutionary algorithms also include a crossover step that has not been considered so far in sequential Monte Carlo methods. A prototypical situation where crossover is needed, or at least could be useful, is multitarget tracking. In multitarget tracking, it may happen that some targets in a multitarget particle are good proxies, but are not going to be selected just because the other targets in the same multitarget particle are bad proxies. This is unfair, and a better design would be to produce shuffled multitarget particles such that the particle for each different target can be replicated from a different multitarget particle. An efficient solution has been proposed in the literature under a posterior independence assumption that unfortunately is almost never met in practical situations. This work provides another solution that does not rely on the posterior independence assumption and that is based on introducing an auxiliary Markov transition in the design. This approach can be seen as an extension of the auxiliary particle filter, and may be of independent interest, outside the application to crossover and to multitarget tracking. Optimization of the design parameters is also addressed.